COSE212: Programming Languages. Lecture 4 Recursive and Higher-Order Programming
|
|
- Clyde McKinney
- 5 years ago
- Views:
Transcription
1 COSE212: Programming Languages Lecture 4 Recursive and Higher-Order Programming Hakjoo Oh 2016 Fall Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
2 Recursive and Higher-Order Programming Heavily used in functional programming languages: Recursive programming provides a powerful problem-solving method. Higher-order programming provides expressiveness. Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
3 Why Recursive Thinking? Describe an algorithm to draw the following: Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
4 Recursive Problem-Solving Strategy If the problem is sufficiently small, directly solve the problem. Otherwise, 1 Split the problem up into smaller problems with the same structure as original. 2 Solve each of those smaller problems. 3 Combine the results to get the overall solution. Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
5 Example: list length If the list is empty, the length is 0. Otherwise, In OCaml: 1 The list can be split into its head and tail. 2 Compute the lengths of the tail. 3 The overall solution is the length of the tail plus one. let rec length l = [] -> 0 hd::tl -> 1 + length tl Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
6 Exercise 1: append Write a function that appends two lists: # append [1; 2; 3] [4; 5; 6; 7];; - : int list = [1; 2; 3; 4; 5; 6; 7] # append [2; 4; 6] [8; 10];; - : int list = [2; 4; 6; 8; 10] Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
7 Exercise 2: reverse Write a function that reverses a given list: val reverse : a list -> a list = <fun> # reverse [1; 2; 3];; - : int list = [3; 2; 1] # reverse ["C"; "Java"; "OCaml"];; - : string list = ["OCaml"; "Java"; "C"] Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
8 Exercise 3: nth-element Write a function that computes nth element of a list: # nth [1;2;3] 0;; - : int = 1 # nth [1;2;3] 1;; - : int = 2 # nth [1;2;3] 2;; - : int = 3 # nth [1;2;3] 3;; Exception: Failure "list is too short". let rec nth l n = [] -> raise (Failure "list is too short") hd::tl -> (*... *) Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
9 Exercise 4: remove-first Write a function that removes the first occurrence of an element from a list: # remove_first 2 [1; 2; 3];; - : int list = [1; 3] # remove_first 2 [1; 2; 3; 2];; - : int list = [1; 3; 2] # remove_first 4 [1;2;3];; - : int list = [1; 2; 3] # remove_first [1; 2] [[1; 2; 3]; [1; 2]; [2; 3]];; - : int list list = [[1; 2; 3]; [2; 3]] let rec remove_first a l = [] -> [] hd::tl -> (*... *) Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
10 Exercise 5: insert Write a function that inserts an element to a sorted list: # insert 2 [1;3];; - : int list = [1; 2; 3] # insert 1 [2;3];; - : int list = [1; 2; 3] # insert 3 [1;2];; - : int list = [1; 2; 3] # insert 4 [];; - : int list = [4] let rec insert a l = [] -> [a] hd::tl -> (*... *) Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
11 Exercise 6: insertion sort Write a function that performs insertion sort: let rec sort l = [] -> [] hd::tl -> insert hd (sort tl) cf) Compare with C-style non-recursive version: for (c = 1 ; c <= n - 1; c++) { d = c; while ( d > 0 && array[d] < array[d-1]) { t = array[d]; } } array[d] array[d-1] = t; d--; = array[d-1]; Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
12 Recursion in ML is Not Expensive In languages like C, recursion should be avoided because function call consumes additional memory: void f() { f(); } /* stack overflow */ The same program in ML iterates forever: let rec f () = f () Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
13 Tail-Recursive Functions More precisely, tail-recursive functions are not expensive in ML. A recursive call is a tail call if there is nothing to do after the function returns. let rec last l = [a] -> a _::tl -> last tl let rec factorial a = if a = 1 then 1 else a * factorial (a - 1) Languages like ML, Scheme, Scala, and Haskell do tail-call optimization, so that tail-recursive calls do not consume additional amount of memory. Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
14 Transforming to Tail-Recursive Functions Non-tail-recursive factorial: let rec factorial a = if a = 1 then 1 else a * factorial (a - 1) Tail-recursive version: let rec fact product counter maxcounter = if counter > maxcounter then product else fact (product * counter) (counter + 1) maxcounter let factorial n = fact 1 1 n Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
15 Higher-Order Functions Higher-order functions: functions that take other functions or return functions as results a powerful tool for code reuse Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
16 Example 1: map Three similar functions: let rec inc_all l = [] -> [] hd::tl -> (hd+1)::(inc_all tl) let rec square_all l = [] -> [] hd::tl -> (hd*hd)::(square_all tl) let rec cube_all l = [] -> [] hd::tl -> (hd*hd*hd)::(cube_all tl) Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
17 Example 1: map The code pattern can be captured by the higher-order function map: let rec map f l = [] -> [] hd::tl -> (f hd)::(map f tl) With map, the functions can be defined as follows: let inc x = x + 1 let inc_all l = map inc l let square x = x * x let square_all l = map square l let cube x = x * x * x let cube_all l = map cube l Or, using nameless functions: let inc_all l = map (fun x -> x + 1) l let square_all l = map (fun x -> x * x) l let cub_all l = map (fun x -> x * x * x) l Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
18 Example 2: fold Two similar functions: let rec sum l = [] -> 0 hd::tl -> hd + (sum tl) let rec prod l = [] -> 1 hd::tl -> hd * (prod tl) # sum [1; 2; 3; 4];; - : int = 10 # prod [1; 2; 3; 4];; - : int = 24 Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
19 Example 2: fold The two functions have the following form: sum [x1; x2;...; xn] = x1 + (x2 + (... + (xn + 0))) prod [x1; x2;...; xn] = x1 * (x2 * (... * (xn * 1))) This pattern is captured by fold: fold f [x1; x2;...; xn] a = f x1 (f x2 (... (f xn a))) let sum lst = fold (fun x y -> x + y) lst 0 let prod lst = fold (fun x y -> x * y) lst 1 or, let sum l = fold (+) l 0 let prod l = fold (*) l 1 Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
20 Example 2: fold The definition of fold: let rec fold f l a = [] -> a hd::tl -> f hd (fold f tl a) Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
21 Exercises Re-write the following functions in one-line using fold: let rec length l = [] -> 0 hd::tl -> 1 + length tl let rec reverse l = [] -> [] hd::tl -> (reverse [hd] let rec is_all_pos l = [] -> true hd::tl -> (hd > 0) && (is_all_pos tl) Hakjoo Oh COSE Fall, Lecture 4 September 27, / 21
COSE212: Programming Languages. Lecture 3 Functional Programming in OCaml
COSE212: Programming Languages Lecture 3 Functional Programming in OCaml Hakjoo Oh 2017 Fall Hakjoo Oh COSE212 2017 Fall, Lecture 3 September 18, 2017 1 / 44 Why learn ML? Learning ML is a good way of
More informationHomework 3 COSE212, Fall 2018
Homework 3 COSE212, Fall 2018 Hakjoo Oh Due: 10/28, 24:00 Problem 1 (100pts) Let us design and implement a programming language called ML. ML is a small yet Turing-complete functional language that supports
More informationCS205: Scalable Software Systems
CS205: Scalable Software Systems Lecture 3 September 5, 2016 Lecture 3 CS205: Scalable Software Systems September 5, 2016 1 / 19 Table of contents 1 Quick Recap 2 Type of recursive solutions 3 Translating
More informationForward recursion. CS 321 Programming Languages. Functions calls and the stack. Functions calls and the stack
Forward recursion CS 321 Programming Languages Intro to OCaml Recursion (tail vs forward) Baris Aktemur Özyeğin University Last update made on Thursday 12 th October, 2017 at 11:25. Much of the contents
More informationF28PL1 Programming Languages. Lecture 14: Standard ML 4
F28PL1 Programming Languages Lecture 14: Standard ML 4 Polymorphic list operations length of list base case: [] ==> 0 recursion case: (h::t) => 1 more than length of t - fun length [] = 0 length (_::t)
More informationPROGRAMMING IN HASKELL. CS Chapter 6 - Recursive Functions
PROGRAMMING IN HASKELL CS-205 - Chapter 6 - Recursive Functions 0 Introduction As we have seen, many functions can naturally be defined in terms of other functions. factorial :: Int Int factorial n product
More informationSchool of Computer Science
A27217 No calculator permitted in this examination School of Computer Science First Year - BSc Artificial Intelligence and Computer Science First Year - BSc Natural Sciences First Year - BSc Computer Science
More informationCSE 341 Lecture 5. efficiency issues; tail recursion; print Ullman ; 4.1. slides created by Marty Stepp
CSE 341 Lecture 5 efficiency issues; tail recursion; print Ullman 3.3-3.4; 4.1 slides created by Marty Stepp http://www.cs.washington.edu/341/ Efficiency exercise Write a function called reverse that accepts
More informationCOSE212: Programming Languages. Lecture 0 Course Overview
COSE212: Programming Languages Lecture 0 Course Overview Hakjoo Oh 2017 Fall Hakjoo Oh COSE212 2017 Fall, Lecture 0 September 4, 2017 1 / 9 Basic nformation nstructor: Hakjoo Oh TAs: Position: Assistant
More informationCS205: Scalable Software Systems
CS205: Scalable Software Systems Lecture 4 September 14, 2016 Lecture 4 CS205: Scalable Software Systems September 14, 2016 1 / 16 Quick Recap Things covered so far Problem solving by recursive decomposition
More informationCVO103: Programming Languages. Lecture 5 Design and Implementation of PLs (1) Expressions
CVO103: Programming Languages Lecture 5 Design and Implementation of PLs (1) Expressions Hakjoo Oh 2018 Spring Hakjoo Oh CVO103 2018 Spring, Lecture 5 April 3, 2018 1 / 23 Plan Part 1 (Preliminaries):
More informationThinking Induc,vely. COS 326 David Walker Princeton University
Thinking Induc,vely COS 326 David Walker Princeton University slides copyright 2017 David Walker permission granted to reuse these slides for non-commercial educa,onal purposes Administra,on 2 Assignment
More informationPoly-HO! COS 326 David Walker Princeton University. polymorphic, higher-order programming
Poly-HO! COS 326 David Walker Princeton University polymorphic, higher-order programming slides copyright 2013-2015 David Walker and Andrew W. Appel permission granted to reuse these slides for non-commercial
More informationCMSC 330, Fall 2013, Practice Problems 3
CMSC 330, Fall 2013, Practice Problems 3 1. OCaml and Functional Programming a. Define functional programming b. Define imperative programming c. Define higher-order functions d. Describe the relationship
More informationUsing Scala in CS241
Using Scala in CS241 Winter 2018 Contents 1 Purpose 1 2 Scala 1 3 Basic Syntax 2 4 Tuples, Arrays, Lists and Vectors in Scala 3 5 Binary output in Scala 5 6 Maps 5 7 Option types 5 8 Objects and Classes
More informationToday s Plan. Programming Languages. Example : Factorial. Recursion. CSE 130 : Spring Lecture 6: Higher-Order Functions
CSE 130 : Spring 2011 Programming Languages Lecture 6: Higher-Order Ranjit Jhala UC San Diego Today s Plan A little more practice with recursion Base Pattern -> Base Expression Induction Pattern -> Induction
More informationTuples. CMSC 330: Organization of Programming Languages. Examples With Tuples. Another Example
CMSC 330: Organization of Programming Languages OCaml 2 Higher Order Functions Tuples Constructed using (e1,..., en) Deconstructed using pattern matching Patterns involve parens and commas, e.g., (p1,p2,
More informationCSE341: Programming Languages Lecture 2 Functions, Pairs, Lists. Dan Grossman Fall 2011
CSE341: Programming Languages Lecture 2 Functions, Pairs, Lists Dan Grossman Fall 2011 Review Building up SML one construct at a time via precise definitions Constructs have syntax, type-checking rules,
More information4. Functional Programming Language-Oriented Programming
4. Functional Programming Language-Oriented Programming Prof. Dr. Bernhard Humm Faculty of Computer Science Hochschule Darmstadt University of Applied Sciences 1 Retrospect: LOP the big picture What is
More informationExample Scheme Function: equal
ICOM 4036 Programming Languages Functional Programming Languages Mathematical Functions Fundamentals of Functional Programming Languages The First Functional Programming Language: LISP Introduction to
More informationChapter 12 Supplement: Recursion with Java 1.5. Mr. Dave Clausen La Cañada High School
Chapter 12 Supplement: Recursion with Java 1.5 La Cañada High School Recursion: Definitions Recursion The process of a subprogram (method) calling itself. A clearly defined stopping state must exist. The
More informationCMSC 330: Organization of Programming Languages. OCaml Higher Order Functions
CMSC 330: Organization of Programming Languages OCaml Higher Order Functions CMSC330 Fall 2017 1 Anonymous Functions Recall code blocks in Ruby (1..10).each { x print x } Here, we can think of { x print
More informationRecap from last time. Programming Languages. CSE 130 : Fall Lecture 3: Data Types. Put it together: a filter function
CSE 130 : Fall 2011 Recap from last time Programming Languages Lecture 3: Data Types Ranjit Jhala UC San Diego 1 2 A shorthand for function binding Put it together: a filter function # let neg = fun f
More informationSome Advanced ML Features
Some Advanced ML Features Mooly Sagiv Michael Clarkson, Cornell CS 3110 Data Structures and Functional Programming University of Washington: Dan Grossman ML is small Small number of powerful constructs
More informationFUNCTIONAL PROGRAMMING
FUNCTIONAL PROGRAMMING Map, Fold, and MapReduce Prof. Clarkson Summer 2015 Today s music: Selections from the soundtrack to 2001: A Space Odyssey Review Yesterday: Lists: OCaml's awesome built-in datatype
More informationIntroduction to OCaml
Fall 2018 Introduction to OCaml Yu Zhang Course web site: http://staff.ustc.edu.cn/~yuzhang/tpl References Learn X in Y Minutes Ocaml Real World OCaml Cornell CS 3110 Spring 2018 Data Structures and Functional
More informationNews. Programming Languages. Recap. Recap: Environments. Functions. of functions: Closures. CSE 130 : Fall Lecture 5: Functions and Datatypes
CSE 130 : Fall 2007 Programming Languages News PA deadlines shifted PA #2 now due 10/24 (next Wed) Lecture 5: Functions and Datatypes Ranjit Jhala UC San Diego Recap: Environments Phone book Variables
More informationChapter 15. Functional Programming Languages
Chapter 15 Functional Programming Languages Copyright 2009 Addison-Wesley. All rights reserved. 1-2 Chapter 15 Topics Introduction Mathematical Functions Fundamentals of Functional Programming Languages
More informationCS Lectures 2-3. Introduction to OCaml. Polyvios Pratikakis
CS 490.40 Lectures 2-3 Introduction to OCaml Polyvios Pratikakis Based on slides by Jeff Foster History ML: Meta Language 1973, University of Edinburg Used to program search tactics in LCF theorem prover
More informationCPS 506 Comparative Programming Languages. Programming Language Paradigm
CPS 506 Comparative Programming Languages Functional Programming Language Paradigm Topics Introduction Mathematical Functions Fundamentals of Functional Programming Languages The First Functional Programming
More informationProblem Set CVO 103, Spring 2018
Problem Set CVO 103, Spring 2018 Hakjoo Oh Due: 06/12 (in class) Problem 1 The Fibonacci numbers can be defined as follows: 0 if n = 0 fib(n) = 1 if n = 1 fib(n 1) + fib(n 2) otherwise Write in OCaml the
More informationFunction definitions. CSE341: Programming Languages Lecture 2 Functions, Pairs, Lists. Example, extended. Some gotchas. Zach Tatlock Winter 2018
Function definitions CSE341: Programming Languages Lecture 2 Functions, Pairs, Lists Zach Tatlock Winter 2018 Functions: the most important building block in the whole course Like Java methods, have arguments
More informationCSE341: Programming Languages Lecture 2 Functions, Pairs, Lists. Zach Tatlock Winter 2018
CSE341: Programming Languages Lecture 2 Functions, Pairs, Lists Zach Tatlock Winter 2018 Function definitions Functions: the most important building block in the whole course Like Java methods, have arguments
More informationCSCI 2041: Tail Recursion and Activation Records
CSCI 2041: Tail Recursion and Activation Records Chris Kauffman Last Updated: Fri Sep 21 14:31:59 CDT 2018 1 Logistics Reading OCaml System Manual: 25.2 (Pervasives Modules) Practical OCaml: Ch 3, 9 Wikipedia:
More informationProgramming Languages. Tail Recursion. CSE 130: Winter Lecture 8: NOT TR. last thing function does is a recursive call
CSE 130: Winter 2010 News Programming Languages Lecture 8: Higher-Order Od Functions Ranjit Jhala UC San Diego Today s Plan Finish Static Scoping Tail Recursion last thing function does is a recursive
More informationFunctional Programming. Introduction To Cool
Functional Programming Introduction To Cool #1 Cunning Plan ML Functional Programming Fold Sorting Cool Overview Syntax Objects Methods Types #2 This is my final day... as your... companion... through
More informationLecture 35: Analysis Review & Tail Recursion 10:00 AM, Nov 28, 2018
Integrated Introduction to Computer Science Klein Lecture 35: Analysis Review & Tail Recursion 10:00 AM, Nov 28, 2018 Contents 1 Append 1 1.1 Implementation....................................... 1 1.2
More informationThe Haskell HOP: Higher-order Programming
The Haskell HOP: Higher-order Programming COS 441 Slides 6 Slide content credits: Ranjit Jhala, UCSD Agenda Haskell so far: First-order functions This time: Higher-order functions: Functions as data, arguments
More informationCSE 341: Programming Languages
CSE 341: Programming Languages Hal Perkins Spring 2011 Lecture 2 Functions, pairs, and lists Hal Perkins CSE341 Spring 2011, Lecture 2 1 What is a programming language? Here are separable concepts for
More informationF# - LISTS. In this method, you just specify a semicolon-delimited sequence of values in square brackets. For example
http://www.tutorialspoint.com/fsharp/fsharp_lists.htm F# - LISTS Copyright tutorialspoint.com In F#, a list is an ordered, immutable series of elements of the same type. It is to some extent equivalent
More informationMP 2 Continuation-Passing Style
MP 2 Continuation-Passing Style CS 421 Fall 2017 Revision 1.1 Assigned September 21, 2017 Due September 28, 2017 23:59pm Extension 48 hours (20% penalty) 1 Change Log 1.1 corrections to 9, 10 and 11 as
More informationIntroduction to Functional Programming
Introduction to Functional Programming Xiao Jia xjia@cs.sjtu.edu.cn Summer 2013 Scheme Appeared in 1975 Designed by Guy L. Steele Gerald Jay Sussman Influenced by Lisp, ALGOL Influenced Common Lisp, Haskell,
More informationInterpreters and Tail Calls Fall 2017 Discussion 8: November 1, 2017 Solutions. 1 Calculator. calc> (+ 2 2) 4
CS 61A Interpreters and Tail Calls Fall 2017 Discussion 8: November 1, 2017 Solutions 1 Calculator We are beginning to dive into the realm of interpreting computer programs that is, writing programs that
More informationCS3110 Spring 2016 Lecture 6: Modules
CS3110 Spring 2016 Lecture 6: Modules Modules are the O part of OCaml, influenced by objects in Java. We see the evolution: Classic ML, CambridgeML (CAML), and finally OCaml. David McQueen is writing the
More informationCS Lecture 6: Map and Fold. Prof. Clarkson Fall Today s music: Selections from the soundtrack to 2001: A Space Odyssey
CS 3110 Lecture 6: Map and Fold Prof. Clarkson Fall 2014 Today s music: Selections from the soundtrack to 2001: A Space Odyssey Review Features so far: variables, operators, let expressions, if expressions,
More informationINF121: Functional Algorithmic and Programming
INF121: Functional Algorithmic and Programming Lecture 6: Polymorphism, Higher-order, and Currying Academic Year 2011-2012 In the previous episodes of INF 121 Basic Types: Booleans, Integers, Floats, Chars,
More informationProgramming Languages
CSE 130: Fall 2009 Programming Languages Lecture 2: A Crash Course in ML News On webpage: Suggested HW #1 PA #1 (due next Fri 10/9) Technical issues installing Ocaml - should be resolved soon! Ranjit Jhala
More informationFall 2017 December 4, Scheme. Instructions
CS 61A Final Review Fall 2017 December 4, 2017 Instructions Form a small group. Start on the first problem. Check off with a helper or discuss your solution process with another group once everyone understands
More informationCMSC 330: Organization of Programming Languages. OCaml Higher Order Functions
CMSC 330: Organization of Programming Languages OCaml Higher Order Functions CMSC 330 - Spring 2017 1 Anonymous Functions Recall code blocks in Ruby (1..10).each { x print x } Here, we can think of { x
More informationCMSC 330: Organization of Programming Languages. Functional Programming with Lists
CMSC 330: Organization of Programming Languages Functional Programming with Lists CMSC330 Spring 2018 1 Lists in OCaml The basic data structure in OCaml Lists can be of arbitrary length Implemented as
More informationIntroduction to OCaml
Introduction to OCaml Jed Liu Department of Computer Science Cornell University CS 6110 Lecture 26 January 2009 Based on CS 3110 course notes and an SML tutorial by Mike George Jed Liu Introduction to
More informationCSE11 Lecture 20 Fall 2013 Recursion
CSE11 Lecture 20 Fall 2013 Recursion Recursion recursion: The definition of an operation in terms of itself. Solving a problem using recursion depends on solving smaller or simpler occurrences of the same
More informationCMSC 330: Organization of Programming Languages. OCaml Higher Order Functions
CMSC 330: Organization of Programming Languages OCaml Higher Order Functions CMSC 330 - Summer 2017 1 Anonymous Functions Recall code blocks in Ruby (1..10).each { x print x } Here, we can think of { x
More informationMap and Fold. Prof. Clarkson Fall Today s music: Selections from the soundtrack to 2001: A Space Odyssey
Map and Fold Prof. Clarkson Fall 2015 Today s music: Selections from the soundtrack to 2001: A Space Odyssey Question How much progress have you made on A1? A. I'm still figuring out how Enigma works.
More informationFun facts about recursion
Outline examples of recursion principles of recursion review: recursive linked list methods binary search more examples of recursion problem solving using recursion 1 Fun facts about recursion every loop
More informationAbstraction and Specification
Abstraction and Specification Prof. Clarkson Fall 2017 Today s music: "A Fifth of Beethoven" by Walter Murphy Review Previously in 3110: Language features for modularity Some familiar data structures Today:
More informationCS Lecture 6: Map and Fold. Prof. Clarkson Spring Today s music: Selections from the soundtrack to 2001: A Space Odyssey
CS 3110 Lecture 6: Map and Fold Prof. Clarkson Spring 2015 Today s music: Selections from the soundtrack to 2001: A Space Odyssey Review Course so far: Syntax and semantics of (most of) OCaml Today: No
More informationCS 321 Programming Languages
CS 321 Programming Languages Intro to OCaml Lists Baris Aktemur Özyeğin University Last update made on Monday 2 nd October, 2017 at 19:27. Some of the contents here are taken from Elsa Gunter and Sam Kamin
More informationProgramming Languages
CSE 130 : Winter 2009 Programming Languages News PA 2 out, and due Mon 1/26 5pm Lecture 5: Functions and Datatypes t UC San Diego Recap: Environments Phone book Variables = names Values = phone number
More informationCunning Plan. One-Slide Summary. Functional Programming. Functional Programming. Introduction to COOL #1. Classroom Object-Oriented Language
Functional Programming Introduction to COOL #1 Cunning Plan Functional Programming Types Pattern Matching Higher-Order Functions Classroom Object-Oriented Language Methods Attributes Inheritance Method
More informationStructure and Interpretation of Computer Programs
CS 61A Summer 2014 Structure and Interpretation of Computer Programs Final Solutions INSTRUCTIONS ˆ You have 3 hours to complete the exam. ˆ The exam is closed book, closed notes, and closed electronics,
More informationProgramming Languages
CSE 130 : Fall 2008 Programming Languages Lecture 6: Datatypes t and Recursion Ranjit Jhala UC San Diego News PA 2 Due Fri (and PA3 up) PA3 is a bit difficult, but do it yourself, or repent in the final
More informationCS 11 Ocaml track: lecture 2
Today: CS 11 Ocaml track: lecture 2 comments algebraic data types more pattern matching records polymorphic types ocaml libraries exception handling Previously... ocaml interactive interpreter compiling
More informationCMSC 330, Fall 2013, Practice Problem 3 Solutions
CMSC 330, Fall 2013, Practice Problem 3 Solutions 1. OCaml and Functional Programming a. Define functional programming Programs are expression evaluations b. Define imperative programming Programs change
More informationWeek - 03 Lecture - 18 Recursion. For the last lecture of this week, we will look at recursive functions. (Refer Slide Time: 00:05)
Programming, Data Structures and Algorithms in Python Prof. Madhavan Mukund Department of Computer Science and Engineering Indian Institute of Technology, Madras Week - 03 Lecture - 18 Recursion For the
More informationCOMP-202: Foundations of Programming. Lecture 13: Recursion Sandeep Manjanna, Summer 2015
COMP-202: Foundations of Programming Lecture 13: Recursion Sandeep Manjanna, Summer 2015 Announcements Final exams : 26 th of June (2pm to 5pm) @ MAASS 112 Assignment 4 is posted and Due on 29 th of June
More informationCMSC330 Spring 2014 Midterm 2 Solutions
CMSC330 Spring 2014 Midterm 2 Solutions 1. (16 pts) OCaml Types and Type Inference Give the type of the following OCaml expressions: a. (2 pts) fun b -> b + 8 Type = int -> int b. (3 pts) fun b -> b 8
More informationCIS 120 Midterm I October 2, Name (printed): Username (login id):
CIS 120 Midterm I October 2, 2015 Name (printed): Username (login id): My signature below certifies that I have complied with the University of Pennsylvania s Code of Academic Integrity in completing this
More informationMini-ML. CS 502 Lecture 2 8/28/08
Mini-ML CS 502 Lecture 2 8/28/08 ML This course focuses on compilation techniques for functional languages Programs expressed in Standard ML Mini-ML (the source language) is an expressive core subset of
More informationShell CSCE 314 TAMU. Functions continued
1 CSCE 314: Programming Languages Dr. Dylan Shell Functions continued 2 Outline Defining Functions List Comprehensions Recursion 3 A Function without Recursion Many functions can naturally be defined in
More informationCS159. Nathan Sprague. November 9, 2015
CS159 Nathan Sprague November 9, 2015 Recursive Definitions Merriam Websters definition of Ancestor: Ancestor One from whom a person is descended [...] Here is a recursive version: Ancestor One s parent.
More informationCMSC330 Fall 2014 Midterm 2 Solutions
CMSC330 Fall 2014 Midterm 2 Solutions 1. (5 pts) General. For the following multiple choice questions, circle the letter(s) on the right corresponding to the best answer(s) to each question. a. In the
More informationCSCI 2041: Lists and Recursion
CSCI 2041: Lists and Recursion Chris Kauffman Chris Kauffman Last Updated: Sun Dec 16 21:13:29 CST 2018 1 Logistics :BMCOL:B block : OCaml System Manual: 1.1-1.3 Practical OCaml: Ch 1-2 OCaml System Manual:
More informationINTERPRETERS 8. 1 Calculator COMPUTER SCIENCE 61A. November 3, 2016
INTERPRETERS 8 COMPUTER SCIENCE 61A November 3, 2016 1 Calculator We are beginning to dive into the realm of interpreting computer programs that is, writing programs that understand other programs. In
More informationTAIL CALLS, ITERATORS, AND GENERATORS 11
TAIL CALLS, ITERATORS, AND GENERATORS 11 COMPUTER SCIENCE 61A November 13, 214 1 Tail Calls Scheme implements tail-call optimization, which allows programmers to write recursive functions that use a constant
More informationRecursion. Garfield AP Computer Science. As usual, significant borrowings from Stuart Reges and Marty Stepp at UW -- thanks!!
Recursion Garfield AP Computer Science As usual, significant borrowings from Stuart Reges and Marty Stepp at UW -- thanks!! Definitions recursion: The definition of an operation in terms of itself. Solving
More informationCSE 143 Lecture 10. Recursion
CSE 143 Lecture 10 Recursion slides created by Marty Stepp and Alyssa Harding http://www.cs.washington.edu/143/ Recursion Iteration: a programming technique in which you describe actions to be repeated
More informationThinking Induc,vely. COS 326 David Walker Princeton University
Thinking Induc,vely COS 326 David Walker Princeton University slides copyright 2013-2015 David Walker and Andrew W. Appel permission granted to reuse these slides for non-commercial educa,onal purposes
More informationHigher-Order Functions
Higher-Order Functions Tjark Weber Functional Programming 1 Based on notes by Pierre Flener, Jean-Noël Monette, Sven-Olof Nyström Tjark Weber (UU) Higher-Order Functions 1 / 1 Tail Recursion http://xkcd.com/1270/
More informationRecursion. What is Recursion? Simple Example. Repeatedly Reduce the Problem Into Smaller Problems to Solve the Big Problem
Recursion Repeatedly Reduce the Problem Into Smaller Problems to Solve the Big Problem What is Recursion? A problem is decomposed into smaller sub-problems, one or more of which are simpler versions of
More informationLab 10: OCaml sequences, comparators, stable sorting 12:00 PM, Nov 12, 2017
Integrated Introduction to Computer Science Hughes Lab 10: OCaml sequences, comparators, stable sorting 12:00 PM, Nov 12, 2017 Contents 1 A last OCaml type, and its utility 1 1.1 Sequences in OCaml....................................
More informationCSE341: Programming Languages Lecture 6 Nested Patterns Exceptions Tail Recursion. Zach Tatlock Winter 2018
CSE341: Programming Languages Lecture 6 Nested Patterns Exceptions Tail Recursion Zach Tatlock Winter 2018 Nested patterns We can nest patterns as deep as we want Just like we can nest expressions as deep
More informationALGORITHM 2-1 Solution for Exercise 4
Chapter 2 Recursion Exercises 1. a. 3 * 4 = 12 b. (2 * (2 * fun1(0) + 7) + 7) = (2 * (2 * (3 * 0) + 7) + 7) = 21 c. (2 * (2 * fun1(2) + 7) + 7) = (2 * (2 * (3 * 2) + 7) + 7) = 45 2. a. 3 b. (fun2(2, 6)
More informationBegin at the beginning
Begin at the beginning Expressions (Syntax) Exec-time Dynamic Values (Semantics) Compile-time Static Types 1. Programmer enters expression 2. ML checks if expression is well-typed Using a precise set of
More informationIntroduction to Delimited Continuations. Typing Printf. Printf. Kenichi Asai. Ochanomizu University. April 13, 2008
Introduction to Delimited Continuations Typing Printf Printf Kenichi Asai Ochanomizu University April 13, 2008 Outline of the talk times (introduction) (1) in Direct Style with exception (2) in Continuation-Passing
More informationProgramming Languages
CSE 130 : Fall 2008 Programming Languages Lecture 2: A Crash Course in ML Ranjit Jhala UC San Diego News On webpage: Suggested HW #1, sample for Quiz #1 on Thu PA #1 (due next Fri 10/10) No make-up quizzes
More informationName: Pennkey: CIS 120 Midterm II November 18, 2011
Name: Pennkey: CIS 120 Midterm II November 18, 2011 1 /20 2 /20 3 /20 4 /20 5 /20 Total /100 Do not begin the exam until you are told to do so. You have 50 minutes to complete the exam. There are 100 total
More informationLecture 19: Recursion
Lecture 19: Recursion Building Java Programs: A Back to Basics Approach by Stuart Reges and Marty Stepp Copyright (c) Pearson 2013. All rights reserved. Recursion recursion: The definition of an operation
More informationCPL 2016, week 10. Clojure functional core. Oleg Batrashev. April 11, Institute of Computer Science, Tartu, Estonia
CPL 2016, week 10 Clojure functional core Oleg Batrashev Institute of Computer Science, Tartu, Estonia April 11, 2016 Overview Today Clojure language core Next weeks Immutable data structures Clojure simple
More informationRecursion & Iteration
Recursion & Iteration York University Department of Computer Science and Engineering 1 Overview Recursion Examples Iteration Examples Iteration vs. Recursion Example [ref.: Chap 5,6 Wilensky] 2 Recursion
More informationCSCC24 Functional Programming Scheme Part 2
CSCC24 Functional Programming Scheme Part 2 Carolyn MacLeod 1 winter 2012 1 Based on slides from Anya Tafliovich, and with many thanks to Gerald Penn and Prabhakar Ragde. 1 The Spirit of Lisp-like Languages
More informationThis assignment has four parts. You should write your solution to each part in a separate file:
Data Structures and Functional Programming Problem Set 1 CS 3110, Fall 013 Due at 11:59 PM, Thursday, September 5 Version: 3 Last Modified: Wednesday, August 8 This assignment has four parts. You should
More informationG Programming Languages - Fall 2012
G22.2110-003 Programming Languages - Fall 2012 Lecture 4 Thomas Wies New York University Review Last week Control Structures Selection Loops Adding Invariants Outline Subprograms Calling Sequences Parameter
More informationFunctional Programming. Pure Functional Programming
Functional Programming With examples in F# Pure Functional Programming Functional programming involves evaluating expressions rather than executing commands. Computation is largely performed by applying
More informationIntroduction to ML. Mooly Sagiv. Cornell CS 3110 Data Structures and Functional Programming
Introduction to ML Mooly Sagiv Cornell CS 3110 Data Structures and Functional Programming The ML Programming Language General purpose programming language designed by Robin Milner in 1970 Meta Language
More informationLists. Prof. Clarkson Fall Today s music: "Blank Space" by Taylor Swift
Lists Prof. Clarkson Fall 2017 Today s music: "Blank Space" by Taylor Swift I could show you incredible things // Magic, madness, heaven, sin So it's gonna be forever // Or it's gonna go down in flames
More informationLecture: Functional Programming
Lecture: Functional Programming This course is an introduction to the mathematical foundations of programming languages and the implementation of programming languages and language-based tools. We use
More informationList Processing in Ocaml
CS251 Programming Languages Handout # 14 Prof. Lyn Turbak February 2, 2007 Wellesley College List Processing in Ocaml Given a list of integers ns, suppose we want to return a new list of the same length
More informationRecursion: Factorial (1) Recursion. Recursion: Principle. Recursion: Factorial (2) Recall the formal definition of calculating the n factorial:
Recursion EECS2030: Advanced Object Oriented Programming Fall 2017 CHEN-WEI WANG Recursion: Factorial (1) Recall the formal definition of calculating the n factorial: 1 if n = 0 n! = n (n 1) (n 2) 3 2
More informationFall 2017 December 4, 2017
CS 61A Final Review Fall 2017 December 4, 2017 Instructions Form a small group. Start on the first problem. Check off with a helper or discuss your solution process with another group once everyone understands
More information